Question 72681
Since nobody else has taken a shot at this, I'll give it a go ...
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{{{dB = 10*log((I/10^(-12)))}}}
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is the equation that governs the relationship between sound intensity and decibels.
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I think what you meant for the given sound intensity was {{{5.4*10^(-10)}}}
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The units of your given intensity and the units of the intensity in the decibel equation 
are consistent, so we can just substitute {{{5.4*10^(-10)}}}  for I in the decibel
equation without having to make any conversion in units.  With this substitution the decibel 
equation becomes:
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{{{dB = 10*log((5.4*10^(-10)/10^(-12)))}}}
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We can now divide the {{{10^(-12)}}} of the denominator into the {{{10^(-10)}}} of the 
denominator.  Recall that when you divide, you subtract exponents.  The subtraction
of the exponents involves {{{(-10)-(-12)}}} and this reduces to {{{-10+12 =2}}}. Therefore,
the decibel equation becomes:
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{{{dB = 10*log((5.4*10^(2)))}}}
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The rules of logarithms say that if you have the log of a product, you can split this into
the sum of the logs of each of the terms in the product.  Applying this rule gives us:
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{{{dB = 10*(log((5.4)) + log((10^(2))))}}}
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The rule of exponents for logarithms says that an exponent comes out as the multiplier 
of the log.  So {{{log ((10^(2)))}}} becomes {{{2*log ((10))}}}.  But {{{log((10))}}} is simply 1,
and therefore, {{{log((10^(2)))}}} reduces just to {{{2}}}. Substitute this back into the 
decibel equation and you get:
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{{{dB = 10*(log((5.4)) + 2)}}}
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Finding the {{{log((5.4))}}} is just a calculator problem.  It is {{{0.732393759}}} or just  round it
to {{{0.732}}} which is probably close enough for your needs.  
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Substituting this value makes the equation:
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{{{dB = 10*(0.732 + 2) = 10*2.732 = 27.32 }}}
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So the answer appears to be 27.32 dB
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Hope you could follow this through and that it helps you to understand this power ratio
equation.